US10047759B2 - Method for controlling the speed of cryogenic compressors arranged in series for cooling cryogenic helium - Google Patents

Method for controlling the speed of cryogenic compressors arranged in series for cooling cryogenic helium Download PDF

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US10047759B2
US10047759B2 US15/322,752 US201515322752A US10047759B2 US 10047759 B2 US10047759 B2 US 10047759B2 US 201515322752 A US201515322752 A US 201515322752A US 10047759 B2 US10047759 B2 US 10047759B2
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compressor
actual
pressure ratio
total pressure
capacity
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US20170152855A1 (en
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Andres Kündig
Can Üresin
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Linde GmbH
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
    • F04D27/004—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids by varying driving speed
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D17/00—Radial-flow pumps, e.g. centrifugal pumps; Helico-centrifugal pumps
    • F04D17/08—Centrifugal pumps
    • F04D17/10—Centrifugal pumps for compressing or evacuating
    • F04D17/12—Multi-stage pumps
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D19/00—Axial-flow pumps
    • F04D19/02—Multi-stage pumps
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D23/00—Other rotary non-positive-displacement pumps
    • F04D23/001—Pumps adapted for conveying materials or for handling specific elastic fluids
    • F04D23/003—Pumps adapted for conveying materials or for handling specific elastic fluids of radial-flow type
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D23/00—Other rotary non-positive-displacement pumps
    • F04D23/001—Pumps adapted for conveying materials or for handling specific elastic fluids
    • F04D23/005—Pumps adapted for conveying materials or for handling specific elastic fluids of axial-flow type
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D25/00—Pumping installations or systems
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
    • F04D27/001—Testing thereof; Determination or simulation of flow characteristics; Stall or surge detection, e.g. condition monitoring
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
    • F04D27/02—Surge control
    • F04D27/0261—Surge control by varying driving speed
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
    • F04D27/02—Surge control
    • F04D27/0269—Surge control by changing flow path between different stages or between a plurality of compressors; load distribution between compressors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B1/00—Compression machines, plants or systems with non-reversible cycle
    • F25B1/10—Compression machines, plants or systems with non-reversible cycle with multi-stage compression
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B49/00—Arrangement or mounting of control or safety devices
    • F25B49/02—Arrangement or mounting of control or safety devices for compression type machines, plants or systems
    • F25B49/022—Compressor control arrangements
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B49/00—Arrangement or mounting of control or safety devices
    • F25B49/02—Arrangement or mounting of control or safety devices for compression type machines, plants or systems
    • F25B49/025—Motor control arrangements
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B9/00—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point
    • F25B9/002—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point characterised by the refrigerant
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B9/00—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point
    • F25B9/10—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point with several cooling stages
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B15/00—Systems controlled by a computer
    • G05B15/02—Systems controlled by a computer electric
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D23/00—Other rotary non-positive-displacement pumps
    • F04D23/001—Pumps adapted for conveying materials or for handling specific elastic fluids
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B2600/00—Control issues
    • F25B2600/02—Compressor control
    • F25B2600/025—Compressor control by controlling speed
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B2600/00—Control issues
    • F25B2600/02—Compressor control
    • F25B2600/025—Compressor control by controlling speed
    • F25B2600/0253—Compressor control by controlling speed with variable speed
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B2700/00—Sensing or detecting of parameters; Sensors therefor
    • F25B2700/19—Pressures
    • F25B2700/193—Pressures of the compressor
    • F25B2700/1931—Discharge pressures
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B2700/00—Sensing or detecting of parameters; Sensors therefor
    • F25B2700/19—Pressures
    • F25B2700/193—Pressures of the compressor
    • F25B2700/1933—Suction pressures

Definitions

  • the invention relates to a method for controlling speeds of compressors arranged in series for compressing a fluid, in particular cryogenic helium.
  • Such compressors in particular turbo compressors, are known from the prior art and typically have a shaft having at least one impeller (compressor wheel) or rotor blades directly connected to the shaft, by means of which the fluid is compressed during the rotation of the shaft.
  • the speed of the compressor is understood to mean the number of full rotations (360°) of the shaft about the shaft axis per unit of time.
  • Compressors such as turbo compressors, are subdivided, in particular, into radial compressors and axial compressors. In the case of a radial compressor, the fluid flows in axially to the shaft and is deflected in a radially outward direction. In the case of an axial compressor, however, the fluid to be compressed flows in through the compressor in a direction parallel to the shaft.
  • compressor systems which usually comprise a number of radial compressors and/or turbo compressors, also called turbo blowers.
  • Turbo compressors have a performance map, which limits the mass flow upwards and downwards in case of a given speed and a given suction state at the entry of the compressor.
  • the upper limit is given by reaching the Mach number 1 in the inside of the blade row of the compressor. This limit is referred to as a choke characteristic in the performance map.
  • the efficiency of a compressor in the choke operation drops dramatically.
  • the lower limit is defined by the breakaway of the mass flow rate at the blade edges of the compressor, which appears as vibration and leads to an—undesired—instant pressure equalization above the compressor.
  • This phenomenon is referred to as surging.
  • the corresponding characteristic in the performance map of the compressor is referred to as a pump characteristic or surge characteristic.
  • a return from the surge state to the normal operating state is then possible by means of a bypass, which provides the respective compressor with a sufficiently large mass flow, such that the compressor reassumes operation within the performance map. Nevertheless, said effect is undesirable, since the profitability of the system is adversely affected as a consequence.
  • Radial compressor connected in series are used in various applications for overcoming greater pressure conditions.
  • Each compressor connected in series has its own performance map (also referred to as operation map) and must be controlled such that the compressor operates as efficiently and safely as possible within its performance map.
  • operation map also referred to as operation map
  • a compressor connected in series is, for example, controlled by changing the speed of the compressor, other factors/states around said compressor change as well, such as the intake pressure, or the mass flow, etc., whereby the states around other compressors in the series are affected.
  • the speed controls of turbo compressors convert real values into so-called reduced values. Reduced values are generated by a suitable normalization of dimensionless variables.
  • a dimensionless reduced mass flow can be determined, for example, which is advantageous for model calculations, for example.
  • variable of the speed can be converted into a reduced speed.
  • the variable per se is required (i.e., for example the mass flow or the speed of the compressor), as well as the temperature, the pressure, and the set values (also referred to as design specifications) of the compressors.
  • the set values are the operating conditions of a compressor in which the compressor operates with the greatest efficiency (in the most profitable manner).
  • Compressors have set values, for example, with respect to the speed, the mass flow, the temperature, and the pressure above the respective compressor. The goal is to operate the compressors of the series close to their design points.
  • the calculation of reduced values is described in various turbo machine journals and books (e.g. “Design of Radial Turbomachines—A. Whitfield, N. C. Baines”).
  • Such a multi-step, cryogenic turbo compressor system must be controlled via a very efficient control to enable the stable and uninterrupted operation thereof.
  • Such a control must be capable of controlling each compressor in a manner such that the compressor on the one hand is driven stably and economically in the performance map of the compressor, and furthermore the controller must be designed such that at the same time all other compressors in the series are operating in stable and economical operation states.
  • the model total pressure ratio is calculated based on the actual total pressure ratio and serves in particular to be able to control the operating states of the compressors, even if the capacity factor is at its maximum value or its minimum value, i.e. is in saturation. Said limits are set, for example, by surge or choke operating states.
  • a low capacity factor causes, according to the invention, in particular operating states close to surge states, while a high capacity factor causes in particular operating states close to the choke states.
  • all operating states lying on the surge characteristic or close to the surge line can be assigned to the capacity factor 0, and all operating states, which are in particular on or close to the choke characteristic, can be assigned to a capacity factor of 1.
  • Said operating states are, however, undesirable, such that the value range of the capacity factor is usually limited, such that neither surge operating states nor choke operating states can be achieved.
  • a typical value range of the capacity factor extends in particular from 0.05 to 0.9.
  • pressures currently present at the entry or the output of the respective compressor are referred to as actual pressures.
  • the actual pressures and the temperatures at the compressor can be determined by means of appropriate instruments or methods, wherein in particular the temperatures at the respective entry of the compressors are necessary to calculate the reduced variables such as, for example, the reduced desired speed.
  • the proportional integral value can be determined in the usual manner, in particular using a so-called PI controller.
  • PI controller for that purpose, on the one hand a so-called proportional value and on the other hand an integral value is calculated, wherein the proportional value is in particular proportional to the difference between desired and actual inlet pressure, and the integral value is in particular calculated by means of an integration based on all or some proportional values determined in the past,
  • a reduced desired speed or a reduced speed is to be understood as a reduced variable, as above.
  • said reduced variable For a conversion into a dimensionful (absolute control) variable, said reduced variable must first be re-transformed. This is done based on formulas listed down below.
  • Each compressor is associated with a control function, which establishes the required desired speed based on the actual total pressure ratio and the capacity factor.
  • the basis of each control function is the entirety of all compressor characteristics and the compressibility of the fluid to be compressed.
  • the proportional integral value can be at most as large as the sum of the logarithm of a design total pressure ratio and a choke capacity factor, wherein the choke capacity factor is in particular 1, and wherein the design total pressure ratio is the total pressure ratio that results when all compressors of the series are operated at their design points, wherein the design point of a compressor defines in particular the operating state (for example, represented by a point in the performance map of the compressor), at which operating state the compressor has the highest efficiency.
  • the choke capacity factor is in particular the capacity factor, which would drive a compressor close to or on a choke operating state or a choke characteristic.
  • the capacity factor corresponds to the difference of the proportional integral value and the natural logarithm of the actual total pressure ratio. This is in particular the case if the control of the compressor occurs in a region where the capacity factor is not in saturation.
  • a maximum value and a minimum value for the capacity factor is defined, wherein in particular the maximum value is between 0.8 and 1, preferably at 0.9 and/or wherein the minimum value is preferably between 0 and 0.1, preferably at 0.05.
  • the model total pressure ratio according to the invention corresponds to the actual total pressure ratio multiplied by a saturation function dependent on the capacity factor, wherein the saturation function is in particular 1 when the capacity factor is between the minimum value and the maximum value, and wherein the saturation function is in particular formed by an exponential function of the difference of the capacity factor and the minimum value when the capacity factor is less than the minimum value, and the saturation function is in particular given by an exponential function of the difference of the capacity factor and the maximum value when the capacity factor is greater than the maximum value.
  • Said modification of the model total pressure ratio ensures that in operating states in which the capacity factor is in saturation, the control continues to impact the compressor, because then instead of the capacity factor, the model total pressure ratio is changed, such that the control function can invoke reduced desired speeds that lead out of said operating states.
  • the capacity factor is equated with the maximum value (in particular after the model total pressure ratio was determined), if the capacity factor is greater than the maximum value. Furthermore, if the capacity factor is less than the minimum value, the capacity factor is preferably equated to the minimum value (in particular after the model total pressure ratio was determined). This serves, in particular, to prevent capacity factors from being given to the control function, which would possibly be harmful for the operation of the compressor. Consequently,
  • the discharge temperature of the fluid at the output of the respective compressor is equal to the inlet temperature of the fluid at the entry of the compressor of the series respectively arranged downstream of the respective compressor
  • the discharge pressure of the fluid at the output of the respective compressor is substantially equal to the inlet pressure of the fluid at the entry of the compressor of the series respectively arranged downstream of the respective compressor.
  • Deviations between the said temperatures may occur, for example, due to heat impact from the environment, etc.
  • Deviations between said pressures may arise, for example, due to pressure losses along the pipelines.
  • the outlet temperature and the outlet pressure for each compressor according to the invention is determined based on the inlet pressure and the inlet temperature of the compressor of the series arranged the furthest upstream, in particular by means of a turbo machine equation and in particular pre-calculated, such that in particular the reduced speed for each compressor and a reduced mass flow are determined by the respective compressor as a function of the total pressure ratio, and in particular of the capacity factor, wherein the overall pressure ratio is then, in the same manner as the actual total pressure ratio, by the quotient of the outlet pressure of the compressor arranged the furthest downstream and the inlet pressure of the compressor of the series arranged the furthest upstream.
  • Establishing reduced desired speeds during operation is greatly simplified by creating a table (a so-called look-up table).
  • the reduced mass flow is a reduced variable, as is the reduced speed, which implicitly includes the temperature of the mass flow through a transformation of the (real or absolute) mass flow.
  • the reduced mass flow can therefore change in particular as a function of the temperature.
  • Turbo machine equations are flow equations that are especially suitable for the description of flows in turbo machines, which also includes compressors. Said turbo machine equations are so-called Euler equations, in particular Euler turbo machine equations or Euler turbo compressor equations.
  • each capacity line is a function for each compressor of the total pressure ratio and in particular a function of the reduced mass flow and of the reduced speed of the respective compressor, and wherein the capacity factor along the respective capacity line for each compressor is in particular constant.
  • the control function establishes the reduced desired speed for each compressor based on a pre-calculated table, wherein the table for each capacity factor, which lies on a capacity line, and for each total pressure ratio, comprises the respective reduced speed, and wherein in particular for capacity factors as well as for total pressure ratios, which are not listed in the table, the corresponding values for the reduced speeds of the respective compressor are established by means of an interpolation method.
  • an interpolation method is, for example, a “nearest neighbor” interpolation.
  • Such a table can, in this context, in particular also be considered a function.
  • the control function can also be given by polynomials, in which the polynomials define in particular the progress of the capacity lines.
  • the capacity lines display those value pairs consisting of the reduced mass flow and of the reduced speed that effect the equalization of the actual inlet pressure and the desired inlet pressure when the control function of the model total pressure ratio and the capacity factor determine a reduced desired speed for each compressor, in particular from the pre-calculated table, and the control is performed by means of the established reduced speeds.
  • the capacity lines are arranged between a surge characteristic and a choke characteristics, wherein the surge characteristic comprises operating states of the respective compressor, where—in case of a given reduced speed and a given reduced mass flow—an individual pressure ratio to be achieved cannot be maintained, and wherein the choke characteristic comprises operational states of the compressor, in which—in the case of a determined reduced desired revolution speed of the respective compressor—a reduction of the respective individual pressure ratio does not result in an increased mass flow through the respective compressor.
  • the individual pressure ratio of a compressor corresponds to the quotient of the discharge pressure at the output of the respective compressor and the inlet pressure at the entry of each compressor.
  • FIG. 1 Performance map with capacity lines of a first compressor, which is arranged the furthest upstream of four compressors connected in series.
  • FIG. 2 Performance map with capacity lines of a second compressor, which is arranged downstream of the first compressor;
  • FIG. 3 Performance map with capacity lines of a third compressor, which is arranged downstream of the second compressor;
  • FIG. 4 Performance map with capacity lines of a fourth compressor, which is arranged downstream of the third compressor;
  • FIG. 5 Control field with the capacity lines of FIG. 1 for the first compressor
  • FIG. 6 Control field with the capacity lines of FIG. 2 for the second compressor
  • FIG. 7 Control field with the capacity lines of FIG. 3 for the third compressor
  • FIG. 8 Control field with the capacity lines of FIG. 4 for the fourth compressor
  • FIG. 9 Performance map with evenly distributed capacity lines of the first compressor of the compressors connected in series;
  • FIG. 10 Performance map with evenly distributed capacity lines of the second compressor
  • FIG. 11 Performance map with evenly distributed capacity lines of the third compressor
  • FIG. 12 Performance map with evenly distributed capacity lines of the fourth compressor
  • FIG. 13 Control field with the capacity lines of FIG. 9 for the first compressor
  • FIG. 14 Control field with the capacity lines of FIG. 10 for the second compressor
  • FIG. 15 Control field with the capacity lines of FIG. 11 for the third compressor
  • FIG. 16 Control field with the capacity lines of FIG. 12 for the fourth compressor
  • FIG. 17 Plugging chart for carrying out the method according to the invention.
  • FIG. 18 Flow chart for the determination of the capacity factor and of the model total pressure ratio.
  • FIG. 19 Establishing a capacity line in the performance map of compressor V 1
  • FIGS. 1 to 4 show performance maps of four compressors V 1 , V 2 , V 3 , V 4 connected in series for the compression of cryogenic helium in the area around 4K.
  • the method according to the invention can also be used for the control of more or less than four compressors, depending on the total pressure ratio that is to be generated. Below a series arrangement of four compressors V 1 , V 2 , V 3 , V 4 is being discussed as an example.
  • the performance map of a compressor represents operating states of the compressor, which operating states can be described by a reduced mass flow and an individual pressure ratio assigned to said reduced mass flow, wherein each operating state is assigned a desired speed in the performance map, which desired speed is required to achieve the operating state.
  • Such a performance map can be created for each compressor or is available for each compressor.
  • a performance map can be created by measuring a plurality of different operating states and thereby characterizing the performance map, or also by a suitable software, which can display the compressor virtually.
  • the helium e.g., is compressed from approximately 15 mbar to 600 mbar. That is, around the design point (operating state for which the compressor series or the compressor system is designed) the compressor system has a total pressure ratio of approximately 40 (600 mbar/15 mbar).
  • the specific distribution of the capacity lines X 00 , X 02 , X 059 X 07 , X 10 in the respective performance map of the compressor ensures that an increase of the capacity factor X generally leads to an increase in the total surge performance, such that a stable system operation is guaranteed.
  • the transverse dotted lines represent states that show the same reduced speeds n 1 , n 2 , n 3 , n 4 of the respective compressor V 1 , V 2 , V 3 , V 4 .
  • the compressors V 1 , V 2 , V 3 , V 4 are run on the same capacity lines X 00 , X 02 , X 05 , X 07 X 10 in each of the performance maps or control fields assigned to the respective compressor. I.e. that all compressors are run with the same capacity factor X.
  • the discharge state, in particular the discharge pressure p 1 and the discharge temperature T 1 of the first compressor V 1 represent the inlet state of the second compressor V 2 .
  • the discharge state of the second compressor V 2 represents the inlet state of the third compressor V 3 and the discharge state of the third compressor V 3 in turn represents the inlet state of the fourth compressor V 4 .
  • the product of the individual pressure ratios q 1 , q 2 , q 3 , q 4 forms the actual total pressure ratio ⁇ actual .
  • the distribution of the actual total pressure ratio ⁇ actual across the compressor series changes.
  • the different capacity factors X influence the distribution of the individual pressure ratios q 1 , q 2 , q 3 , q 4 via the respective compressors V 1 , V 2 , V 3 , V 4 , which are composed differently, according to each capacity factor X, whereby the common mass flow changes throughout all compressors V 1 , V 2 , V 3 , V 4 of the series.
  • FIG. 1 shows the performance map of the first compressor V 1 of the series arrangement of the four compressors V 1 , V 2 , V 3 , V 4 with the five capacity lines X 00 , X 02 , X 05 , X 07 , X 10 .
  • the capacity line X 00 is located on the surge characteristic S.
  • the capacity factor X which is passed to the control function F, is limited to a minimum value X min of 0.05, if necessary.
  • the capacity line X 10 is not located on the choke characteristic C of compressor V 1 .
  • FIG. 2 shows the performance map of the second compressor V 2 of compressors V 1 , V 2 , V 3 , V 4 arranged in series.
  • the capacity line X 00 is located on the surge characteristic S and the capacity lines X 05 , X 07 and X 10 run similarly as in the performance map of compressor V 1 . Only the capacity line X 02 runs further to the left here, close to capacity line X 00 .
  • FIG. 3 shows the performance map of the third compressor V 3 of compressors V 1 , V 2 , V 3 , V 4 arranged in series.
  • the capacity line X 05 runs in the left area of the performance map here.
  • FIG. 4 shows the performance map of the fourth compressor V 4 of compressors V 1 , V 2 , V 3 , V 4 arranged in series of the compressor system.
  • the capacity lines X 00 , X 02 , X 05 , X 07 are concentrated around the surge characteristic S.
  • the reduced desired speeds n 1 , n 2 , n 3 , n 4 for these capacity factors are calculated comparatively close to the so-called surge speed, that is, the reduced speed n 4 , at which compressor V 4 moves into the surge state.
  • said reduced desired speeds n 4 are limited to a range between 90-95% of the surge speed.
  • FIGS. 5 to 8 show control fields of compressors V 1 , V 2 , V 3 , V 4 .
  • the reduced speed n 1 , n 2 , n 3 , n 4 is applied as a function of the natural logarithm of the total pressure ratio ⁇ .
  • the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 are recorded in the control field, the run of which lines and their distribution are in particular predefined by the run and the distribution of the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 in the performance maps of compressors V 1 , V 2 , V 3 , V 4 .
  • a plurality of working points on the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 of the compressor V 1 are arithmetically followed via the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 of all subsequent compressors (V 2 , V 3 and V 4 ) to the system output.
  • This calculation is always based on the assumption that the state of the fluid at the entry of each additional compressor corresponds to the discharge state of the preceding compressor.
  • the total pressure ratio 7 and the associated reduced speeds n 1 , n 2 , n 3 , n 4 are determined.
  • the reduced (desired) speeds n 2 , n 3 , n 4 for the respective compressor can be determined for each given value pair consisting of the capacity factor X and the total pressure ratio ⁇ .
  • These reduced (desired) speeds n 1 , n 2 , n 3 , n 4 are converted by means of measured temperatures into absolute desired speeds.
  • the control function F can be explicitly read from the control field.
  • the method according to the invention is suitable for controlling compressors V 1 , V 2 , V 3 , V 4 , in particular during the equilibrium operation, during which only low or slow inlet pressure fluctuations and discharge pressure fluctuations are to be expected.
  • this method is also suitable for the so-called pump-up (the desired inlet pressure p desired is higher than the actual inlet pressure p actual ), or pump-down (the desired inlet pressure p desired is lower than the actual inlet pressure p actual ) from states that are comparatively far from equilibrium, which is an indicator of the stability of the method.
  • the output pressure p 4 fluctuates between, for example, 450 mbar and 500 mbar.
  • the fluctuations are caused, for example, in the variable mass flow and the subsequent reaction of downstream volumetric machines after the compressor series.
  • the natural logarithm of the actual total pressure ratio ⁇ actual is in the value range of 3.11-3.22.
  • the capacity factor X is about 0.5.
  • the actual discharge pressure p 4 fluctuates between 450 mbar and 500 mbar, i.e. the logarithm of the actual total pressure ratio ⁇ actual fluctuates between 1.5 and 1.6. Due to the high deviation of the actual inlet pressure p actual from the desired inlet pressure p desired the capacity factor X is continuously increased (e.g., from 0.5 to 1).
  • the actual inlet pressure p actual adjusts to the desired inlet pressure p desired , wherein the capacity factor X, depending on the actual total pressure ratio ⁇ actual is adapted, and eventually, when reaching the desired inlet pressure p desired , drops to approximately 0.5 again.
  • this control can be seen as follows:
  • the reduced desired speeds n 1 , n 2 , n 3 , n 4 are (generally) increased for each compressor V 1 , V?, V 3 , V 4 .
  • This causes a change of the total pressure ratio ⁇ actual because an increased reduced mass flow ⁇ dot over (m) ⁇ 1 , ⁇ dot over (m) ⁇ 2 , ⁇ dot over (m) ⁇ 3 , ⁇ dot over (m) ⁇ 4 results as a consequence of the increased speeds n 1 , n 2 , n 3 , n 4 .
  • the actual total pressure ratio ⁇ actual increases, since the actual inlet pressure p actual decreases.
  • An increasing actual total pressure ratio ⁇ actual is now causing a substantially horizontal movement in the control field, such that the capacity factor X is generally down-regulated again. If the actual inlet pressure p actual now corresponds to the desired inlet pressure p desired , the capacity factor X is approximately 0.5. At this value of the capacity factor X and the logarithm of the design total pressure ratio ⁇ design (of, for example, 3.5), the series of compressors is running with the highest efficiency.
  • the actual discharge pressure p 4 fluctuates between 450 mbar and 500 mbar, i.e. the logarithm of the actual total pressure ratio ⁇ actual fluctuates between 3.11 and 3.22. Due to the deviation of the actual inlet pressure to the desired inlet pressure, the capacity factor X is reduced (e.g. from 0.5 to 0).
  • This type of regulation is especially advantageous for operating states or actual total pressure states ⁇ actual close to the design total pressure ratio ⁇ design .
  • the capacity factor X is run in saturation (i.e. 0 or 1, or 0.05 or 0.9), yet the actual total pressure ratio ⁇ actual does not necessarily change, since, for example, two capacity lines X 00 , X 02 , X 05 , X 07 , X 10 overlap at these states.
  • An increase or reduction of the capacity factor X does not result in a change of the reduced desired speed n 1 , n 2 , n 3 , n 4 there.
  • the method according to the invention controls as follows:
  • the actual discharge pressure p 4 is, for example, at 450 mbar, and the actual inlet pressure p actual is at 350 mbar.
  • the logarithm of the actual total pressure ratio ⁇ actual is therefore approximately at 0.25.
  • the desired inlet pressure p desired is 20 mbar.
  • the capacity factor X is thus increased due to the difference between the actual and the desired inlet pressure.
  • FIG. 8 which shows the control field of the fourth compressor V 4 .
  • an increase of the capacity factor X from 0.75 to 1 (or to 0.9, due to the limitation to the maximum value X max ) does not necessarily result in an increase of the reduced desired speed n 4 .
  • the actual total pressure ratio ⁇ actual would not change any further then.
  • the actual total pressure ratio ⁇ actual is replaced or adapted by a model total pressure ratio ⁇ model (cf. above).
  • the model total pressure ratio ⁇ model is slightly larger than the actual total pressure ratio ⁇ actual .
  • movement occurs horizontally along the capacity line X 10 of 1 (or 0.9). Consequently, one moves out of the overlapping region of the capacity lines X 07 and X 10 , such that the control based on the model total pressure ratio ⁇ model and the capacity factor X continues to work effectively.
  • the model total pressure ratio ⁇ model equals the actual total pressure ratio ⁇ actual .
  • FIGS. 9 to 12 show an even distribution of the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 in the performance map for each compressor V 1 , V 2 , V 3 , V 4 .
  • This type of distribution involves several disadvantages, the elimination of which results, for example, in distributions such as shown in FIGS. 1 to 4 .
  • the second and the third compressor V 2 , V 3 ( FIGS. 10 and 11 ) display very high reduced mass flows ⁇ dot over (m) ⁇ 2 , ⁇ dot over (m) ⁇ 3 on top of very high reduced speeds n 2 , n 3 of the respective compressor.
  • the efficiency of the two compressors V 2 , V 3 drops significantly and the discharge temperature increases, thus increasing the risk, in particular at the third compressor V 3 , of a too high speed (overspeed).
  • FIG. 13 shows, however, that during an even distribution of the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 in the performance map, the reduced speeds n 1 in the performance map, for example, for the first compressor V 1 ( FIG. 9 ), are reduced to a pressure ratio of approximately 3 for increasing capacity factors X, which would be an undesired control.
  • the goal is, after all, an increase of the reduced speeds n 1 , in order to reduce the actual inlet pressure p actual .
  • the fourth compressor V 4 has temporarily very high reduced speeds n 4 at low actual total pressure ratios ⁇ actual ( FIG. 16 ). This applies, in particular, to capacity line X 10 . Very high reduced speeds n 1 point to very high speeds and high temperatures, which characterizes an inefficient operational state.
  • FIG. 5 shows that the reduced speeds m from the first compressor V 1 increase along the capacity lines X 02 , X 05 , X 07 and X 10 , in each case in the actual total pressure ratio ⁇ actual . Thereby, the undisturbed operation of the most important compressor with the highest single pressure ratio is ensured during a pump down.
  • FIGS. 1 to 4 show that no compressor is driven into the choke state (i.e. to the choke characteristic C), thus guaranteeing a high efficiency.
  • FIGS. 5 to 8 show further, that each compressor V 1 , V 2 , V 3 , V 4 , at a certain actual total pressure ratio ⁇ actual (or the logarithm thereof) reaches a reduced desired speed n 1 , n 2 , n 3 , n 4 of 1 and remains in this area.
  • ⁇ actual the fourth compressor V 4
  • the second and third compressors V 2 , V 3 and at high pressure conditions ⁇ actual , as can be found at the design point, the first compressor V 1 ).
  • This behavior ensures an undisturbed pump down and reduces the risk of overspeeding.
  • High capacity factors X do not always lead to higher reduced speeds n 1 , n 2 , n 3 , n 4 , neither at evenly distributed capacity lines X 00 , X 02 , X 05 , X 07 , X 10 , nor at unevenly distributed capacity lines X 00 , X 02 , X 05 , X 07 , X 10 .
  • unevenly distributed capacity lines X 00 , X 02 , X 05 , X 07 , X 10 there is the possibility to achieve a consistent increase of the reduced desired speeds n 1 , n 2 , n 3 , n 4 by increasing the total pressure ratio n to a model total pressure ratio ⁇ model .
  • the criteria for the distribution of the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 in the performance map of each compressor V 1 , V 2 , V 3 , V 4 may be derived from the following principles.
  • the regulation function F for the reduced speeds n 1 , n 2 , n 3 , n 4 is also determined.
  • No compressor is to be operated on the choke or surge characteristic C, S. No compressor must be controlled to an overspeed, since otherwise machine safety is not guaranteed.
  • the compressors V 1 , V 2 , V 3 , V 4 must reach their design points (economic operating states) successively and, upon reaching the design point, the reduced desired speed value n 1 , n 2 , n 3 , should stay around 1 (at a tolerance of approximately 5%). I.e., during low total pressure ratios, the total pressure ratio should be generated by the fourth (last) compressor V 4 of the series, wherein, during an increasing total pressure ratio, when the fourth compressor is already running at the design point, the third compressor V 3 , and in case of a further increase of the total pressure ratio, the second compressor V 2 is connected, and finally the first compressor V 1 , such that in the end all compressors are operated on their respective design points.
  • the compressors with the highest single pressure ratio q 1 , q 2 , q 3 , q 4 must (if possible) display increasing reduced desired speeds n 1 , n 2 , n 3 , n 4 for increasing capacity factors X, such that the control around the design point can be carried out quickly.
  • the first compressor V 1 usually shows the highest single pressure ratio q 1 .
  • the capacity lines X 00 , X 02 , X 05 , X 07 , X 10 must in particular meet the following conditions in the performance map:
  • FIG. 19 shows, using a performance map for the first compressor V 1 as an example, that for a given reduced mass flow ⁇ dot over (m) ⁇ 1 a plurality of individual pressure ratios q 1 is possible.
  • a capacity line for example, capacity line X 05 , then determines how the compressor for a certain capacity factor within the series is to be regulated for the series to work as efficiently as possible. It can be seen that the capacity line X 05 does not run exactly in the center of the maximum and minimum single pressure ratios (marked by circles in FIG. 19 ) that are possible for a given reduced mass flow ⁇ dot over (m) ⁇ 1 .
  • the (absolute) speed is calculated according to the formula for the conversion from reduced to absolute speeds to 600 Hz:
  • n abs n red ⁇ n Design ⁇ T actual T Design
  • n abs is the absolute speed
  • n red is the reduced speed (in this case n 1 )
  • n design is the speed, for which the compressor was designed.
  • TT actual is the actual temperature of the fluid
  • T design is the delivery temperature or design temperature of the compressor.
  • ⁇ dot over (m) ⁇ red is the reduced mass flow through the compressor
  • ⁇ dot over (m) ⁇ ist is the current mass flow
  • ⁇ dot over (m) ⁇ Design refers to the mass flow, for which the respective compressor is designed
  • p design constitutes the design pressure at the respective compressor
  • T design is the design temperature
  • p actual is the actual inlet pressure on the respective compressor.
  • a flow rate is calculated, in particular the tangential flow rate in compressor V 1 .
  • the flow rate can be calculated by means of the fluid density at the output of compressor V 1 .
  • the density is a function of the discharge conditions (in particular of the pressure and the temperature). Therefore, this step is calculated iteratively, as will be explained in the following.
  • the density is assumed to be 0.27 kg/m 3 for example. I.e. based on 16 g/s, the density of 0.27 kg/m 3 and the exit face of the compressor, a flow rate of the fluid can be calculated.
  • a flow angle for example, based on the geometry of the compressor wheel
  • the tangential flow rate is based on the flow rate of the fluid.
  • the enthalpy increase is calculated based on the product of the tangential flow rate and the peripheral speed of the compressor wheel.
  • the enthalpy increase at compressor V 1 is converted into a temperature increase by means of the known heat capacity of the fluid. Furthermore, the efficiency of compressor V 1 at the respective operating state (reduced speed n 1 , reduced mass flow ⁇ dot over (m) ⁇ 1 ) is established in the performance map. The pressure increase results from the temperature increase and the efficiency of the compressor at the respective operating state.
  • discharge temperature T 1 and the discharge pressure P 1 of the first compressor V 1 of the series are established.
  • the density of the fluid is calculated based on these two variables, and then compared with the originally assumed density value. If the density values deviate from one another, the previous steps for calculating the density (in particular by variation of the assumed density) are repeated until the calculated density corresponds to the assumed density.
  • discharge pressure P 1 and discharge temperature T 1 form the inlet state of the subsequent compressor V 2 .
  • tables can be generated by generating a table from each performance map and reading the pressure ratios out of this table as a function of the reduced mass flow and the reduced speed.
  • a PI controller (proportional integral controller) establishes in particular a proportional value prop from the difference between the desired inlet pressure p desired and the actual inlet pressure p actual at the first compressor V 1 of the series.
  • the proportional integral value PI is smaller than the sum of the maximum value of the capacity factor X max and of the natural logarithm of the design total pressure ratio ⁇ design , the capacity factor X is calculated based on the difference of the proportional integral value PI and the natural logarithm of the actual total pressure ratio ⁇ actual . Otherwise, the proportional integral value PI is limited to the sum of the natural logarithm of the design total pressure ratio ⁇ design and the maximum value of the capacity factor X max , in particular for the calculation of the capacity factor X, i.e.:
  • the model total pressure ratio ⁇ model equals the actual total pressure ratio ⁇ actual , when the thus determined capacity factor X lies between the minimum value and the maximum value X min , X max . If the capacity factor X is outside this value range, the model total pressure ratio ⁇ model changes as described above by means of a saturation function.
  • the capacity factor X is limited to its minimum value or maximum value X min , X max , and then, in particular together with the model total pressure ratio ⁇ model passed on to the control function F, which determines the reduced desired speed n 1 , n 2 , n 3 , n 4 for the respective compressor V 1 , V 2 , V 3 , V 4 based on these arguments.
  • the reduced desired speeds n 1 , n 2 , n 3 , n 4 for each compressor V 1 , V 2 , V 3 , V 4 can, in particular, be recorded in a table (look-up table).
  • This table can, in particular, be created by means of model calculations.
  • a software for reading out the reduced desired speeds n 1 , n 2 , n 3 , n 4 from the table can be used.
  • a PID controller instead of a PI controller, a PID (proportional integral derivative) controller can be used. This is in particular advantageous when the mass flow volumes to be controlled are smaller than the volumes in cooling systems of the type described above, as rapid fluctuations in these relatively large volumes are rather rare. When small volumes are to be controlled, it is advantageous to also have a fast-reacting controlling component, such as a PID controller, which reacts faster than a PI controller due to its differentiating component.

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DE102014010104.5A DE102014010104A1 (de) 2014-07-08 2014-07-08 Verfahren zur Regelung der Drehzahl von seriengeschalteten kryogenen Verdichtern zur Kühlung von tiefkaltem, kryogenen Helium
DE102014010104 2014-07-08
PCT/EP2015/001342 WO2016005038A1 (de) 2014-07-08 2015-07-02 Verfahren zur regelung der drehzahl von seriengeschalteten kryogenen verdichtern

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